The Hydrologic
Ensemble Forecast Service or HEFS
combines meteorological and hydrological components
to build an ensemble of forecast stream flows that account
for uncertainty in the meteorology and hydrology.
The Meteorological Ensemble Forecast Processor
or MEFP is the first step in HEFS.
It creates an ensemble of meteorological forecasts
used as inputs to the hydrological model.
The MEFP can use meteorological forecasts from a variety of sources
such as the Global Ensemble Forecast System or GEFS.
The problem is these forecasts from meteorological models
often contain bias and tend to underestimate uncertainty.
To overcome these limitations of the meteorological models,
we use a statistical technique within MEFP that creates its own
ensemble of meteorological forcings for the individual river basins.
These meteorological forcings need to have minimal bias, reliable spread
and realistic patterns in both space
and time.
To achieve this, the MEFP has three steps
build historical error distributions.
Sample these distributions based on the current single-valued
meteorological forecast and create forecast time series from these samples.
In order to explain these steps,
let's walk through a simplified example using temperature.
In this first step, we need to quantify
the bias and uncertainty in past forecasts so that later
we can account for these in the current forecast.
We start with a point that represents a single historical forecast
observation pair for a six hour lead time in a given river basin.
When many historical forecasts are compared with their corresponding
past observations, we obtain a cloud of historical forecast-observation pairs.
This cloud is representative of a single forecast, lead time and river basin.
The cloud can be modeled with a probability distribution
surface, which represents the bias
and the uncertainty in the historical forecasts.
This can be represented as a three-dimensional surface,
which will serve as the historical probability distribution.
We'll use this in the next step to provide information on the past
bias and uncertainty.
Next, we need to sample
the distributions based on the current single-valued meteorological forecast.
Let's say the current GEFS forecast mean temperature for the river
basin of interest at a forecast lead time of 6 hours is 11 degrees Celsius.
Now, how can we find the historical bias and uncertainty
associated with this current forecast value?
If we create a slice through the surface at the current forecast temperature,
we obtain a historically based distribution of observed temperatures.
This represents the uncertainty associated
with the forecast value of 11 degrees Celsius.
Because this probability distribution is based on historical observations,
we've now removed any bias from the current forecast.
However, the hydrological model requires an ensemble of single-valued inputs
rather than probability distributions.
The MEFP provides these single values
by sampling them from the probability distribution.
Here we've sampled only four temperatures from this distribution.
Keep in mind
that HEFS typically samples dozens of temperatures.
The process of generating and sampling from a unique probability
distribution is repeated for each lead time in the forecast.
Next, we need to connect these samples in time to provide multiple time
series of meteorological forcings for the hydrological models.
Our goal is to do this
in such a way that we retain the relationships across time and space,
as well as with other variables such as precipitation.
To do this, MEFP uses a process called the "Schaake Shuffle".
This uses historically observed weather patterns as a guide to connect
the samples.
Since the connections are informed by past historical patterns,
they retain the physical relationships in time and space, as well as
between temperature and precipitation that were observed in the past.
The end product is an ensemble of single valued time series
that retain the temporal,
spatial and intra variable relationships seen in the historical record.
Steps one through three are then repeated for precipitation
to produce ensembles of temperature and precipitation time series.
These are the output of MEFP and the inputs for the next step of HEFS,
which is the hydrological model.
After running the hydrological model using each time series
produced by the MEFP, the HEFS produces an ensemble streamflow forecast.
These ensemble members now reflect a range of streamflow outcomes
based on the historical meteorological forecast uncertainty.
The MEFP component of HEFS
allows us to adjust current temperature and precipitation forecasts
based on the performance of past forecasts.
These adjusted meteorological forecasts are used in the hydrological
forecast model to provide a reliable ensemble of streamflow forecasts.
So at the end of the day,
we can produce a more reliable ensemble streamflow forecast
by adjusting for the known uncertainty
and bias that exist in the meteorological model inputs.
However, these forecasts don't yet account for hydrologic model uncertainties
or correct for hydrologic model bias.
In the next step of the HEFS, the raw ensemble forecasts are adjusted
to account for the hydrological modeling uncertainties and to correct for bias,
using a tool called the ensemble post processor or EnsPost.
EnsPost is explained in a separate video
in this series.